Modeling and simulations of quantum phase slips in ultrathin superconducting wires

TL;DR

This paper models quantum phase slips in ultrathin superconducting wires using a microscopic approach, introducing a Monte Carlo method to analyze QPS tunneling amplitudes and their effects near the superconductor-insulator transition.

Contribution

It develops a direct Monte Carlo simulation method to study QPS tunneling amplitudes beyond the dilute instanton approximation in ultrathin superconducting wires.

Findings

Tunneling amplitude scales near the superconductor-insulator transition.

Voltage-charge relation varies from sinusoidal to complex shapes with QPS density.

Method allows analysis without limitations of QPS density.

Abstract

We study quantum phase slips (QPS) in ultrathin superconducting wires. Starting from an effective one-dimensional microscopic model, which includes electromagnetic fluctuations, we map the problem to a (1+1)-dimensional gas of interacting instantons. We introduce a method to calculate the tunneling amplitude of quantum phase slips directly from Monte Carlo simulations. This allows us to go beyond the dilute instanton gas approximation and study the problem without any limitations of the density of QPS. We find that the tunneling amplitude shows a characteristic scaling behavior near the superconductor-insulator transition. We also calculate the voltage-charge relation of the insulating state, which is the dual of the Josephson current-phase relation in ordinary superconducting weak links. This evolves from a sinusoidal form in the regime of dilute QPS to more exotic shapes for higher QPS densities, where interactions are important.